This inexact prediction is more than an idle curiosity because of the nascent effort of 301Works, under the aegis of the Internet Archive, to preserve re-directs even if, especially if, a URL-shortener goes belly-up or merely stops supporting already-issued links. More than 20 companies have joined 301Works, and bit.ly made this commitment on its corporate blog last November:

In Part I, I calculated that bit.ly is currently using a pool of 62^6 = 56,800,235,584 six-character strings that it can assign as re-directs, for example, to provide URL-shortening for tweets that are up against Twitter’s 140-character limit.